Patchworking singular algebraic curves, non-Archimedean amoebas and enumerative geometry
| dc.creator | Shustin, Eugenii | |
| dc.date | 2002-11-18 | |
| dc.date | 2005-05-13 | |
| dc.date.accessioned | 2026-07-07T04:53:03Z | |
| dc.date.available | 2026-07-07T04:53:03Z | |
| dc.description | We prove a new patchworking theorem for singular algebraic curves, which states the following. Given a complex toric threefold $Y$ which fibers over ${\mathbb C}$ with a reduced reducible zero fiber $Y_0$ and other fibers $Y_t$ smooth, and given a reduced curve $C_0\subset Y_0$, the theorem provides a sufficient condition for the existence of a one-parametric family of curves $C_t\subset Y_t$, which induces an equisingular deformation for some singular points of $C_0$ and certain prescribed deformations for the other singularities. As application we give a comment on a recent theorem by G. Mikhalkin on enumeration of nodal curves on toric surfaces via non-Archimedean amoebas [arXiv:math.AG/0209253]. Namely, using our patchworking theorem, we establish link between nodal curves over the field of complex Puiseux series and their non-Archimedean amoebas, what has been done by Mikhalkin in a different way. We discuss also the case of curves with a cusp as well as real nodal curves. | |
| dc.description | 50 pages, 5 figures | |
| dc.identifier | https://arxiv.org/abs/math/0211278 | |
| dc.identifier | http://arxiv.org/abs/math/0211278 | |
| dc.identifier | Algebra i Analiz 17 (2005), no. 2, 170--214 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65699 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14H15; 12J25; 14H20; 14M25; 14N10 | |
| dc.title | Patchworking singular algebraic curves, non-Archimedean amoebas and enumerative geometry | |
| dc.type | text |